Chordal and Sequentially Cohen-Macaulay Clutters
Chordal and Sequentially Cohen-Macaulay Clutters
We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement …